Extreme learning machine with fuzzy input and fuzzy output for fuzzy regression

It is practically and theoretically significant to approximate and simulate a system with fuzzy inputs and fuzzy outputs. This paper proposes a extreme learning machine (ELM)-based fuzzy regression model (FRELM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm FR}}_{{{\rm ELM}}}$$\end{document}) in which both inputs and outputs are triangular fuzzy numbers. Algorithm for training FRELM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm FR}}_{{{\rm ELM}}}$$\end{document} is designed, and its computational complexity is analyzed. Furthermore, the convergence and error estimation for FRELM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm FR}}_{{{\rm ELM}}}$$\end{document} are discussed. Numerical simulations show that the proposed FRELM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm FR}}_{{{\rm ELM}}}$$\end{document} can effectively approximate a fuzzy input and fuzzy output system.